Richard M. Martin is Emeritus Professor at the University of Illinois, Urbana-Champaign, and Consulting Professor at Stanford University. He has made extensive contributions to the field of modern electronic structure methods and the theory of interacting electron systems and and he is the author of the companion book Electronic Structure: Basic Theory and Methods.

This extensive textbook sets out modern methods of computing properties of materials for graduates and researchers who want to use and understand advanced tools. Including essential theoretical background, practical guidelines and instructive applications, as well as less technical topic overviews for beginners, this book illuminates the mathematics behind the methods.

Preface; Part I. Interacting Electrons: Beyond the Independent-Particle Picture: 1. The many electron problem: introduction; 2. Signatures of electron correlation; 3. Concepts and models for interacting electrons; Part II. Foundations of Theory for Many-Body Systems: 4. Mean fields and auxiliary systems; 5. Correlation functions; 6. Many-body wavefunctions; 7. Particles and quasi-particles; 8. Functionals in many-particle physics; Part III. Many-Body Green's Function Methods: 9. Many-body perturbation theory: expansion in the interaction; 10. Many-body perturbation theory via functional derivatives; 11. The RPA and the GW approximation for the self-energy; 12. GWA calculations in practice; 13. GWA calculations: illustrative results; 14. RPA and beyond: the Bethe-Salpeter equation; 15. Beyond the GW approximation; 16. Dynamical mean field theory; 17. Beyond the single-site approximation in DMFT; 18. Solvers for embedded systems; 19. Characteristic hamiltonians for solids with d and f states; 20. Examples of calculations for solids with d and f states; 21. Combining Green's functions approaches: an outlook; Part IV. Stochastic Methods: 22. Introduction to stochastic methods; 23. Variational Monte Carlo; 24. Projector quantum Monte Carlo; 25. Path integral Monte Carlo; 26. Concluding remarks; Part V. Appendices: A. Second quantization; B. Pictures; C. Green's functions: general properties; D. Matsubara formulation for Green's functions for T ¿= 0; E. Time-ordering, contours, and non-equilibrium; F. Hedin's equations in a basis; G. Unique solutions in Green's function theory; H. Properties of functionals; I. Auxiliary systems and constrained search; J. Derivation of the Luttinger theorem; K. Gutzwiller and Hubbard approaches; References; Index.